I've found one way to "almost" call using Viber - by adding contact:
viber://add?number=0123456789
This will open Viber "Add Contact" dialog, and user can finally call expected number after adding it as a new contact.
Tested this on 5.6 Viber.
Also works from HTML:
<a href="viber://add?number=%2B49150123456789">Viber me</a>
However, if contact doesn't exist, the first click would only open the Dialog, save new contact and go back to your application/page.
Clicking the same link again will open directly contact view with Call out button
Cheers!